The generator matrix

 1  0  1  1  1 X^2+X  1  1  X  X  1
 0  1  1 X^2+X X^2+X+1  1 X^2  X X^2  0  0
 0  0  X  0 X^2+X X^2  X X^2+X  X X^2+X  0
 0  0  0 X^2 X^2 X^2  0  0 X^2  0  0

generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+53x^8+52x^9+141x^10+28x^11+134x^12+44x^13+50x^14+4x^15+4x^16+1x^18

The gray image is a linear code over GF(2) with n=44, k=9 and d=16.
This code was found by Heurico 1.16 in 0.00163 seconds.